We have been going through betta at a rate of about one a week during the 5 weeks. Fish store has tested our water a few times and said it's fine. Any suggestions on what we should do?

Housing
What size is your tank? 10 gallon divided tank
What temperature is your tank?
Does your tank have a filter? yes
Does your tank have an air stone or other type of aeration? no
Is your tank heated? yes
What tank mates does your betta fish live with? 1 betta on each side of divided tank. 2 snails per side.

Food
What type of food do you feed your betta fish? usually pellets; occasionally bloodworms, flakes
How often do you feed your betta fish? 2 times per day (2 pellets)

Maintenance
How often do you perform a water change? once a month
What percentage of the water do you change when you perform a water change? 30-40%
What type of additives do you add to the water when you perform a water change? started adding Prime Chlorine reduce 1 week ago; tap water conditioner, stabilizer

Water Parameters:

Have you tested your water? If so, what are the following parameters?

Ammonia: about 0
Nitrite: other parameters tested at fish store and said to be normal
Nitrate:
pH:
Hardness:
Alkalinity:

Symptoms and Treatment
How has your betta fish's appearance changed? not that we've noticed
How has your betta fish's behavior changed? After 4-5 days, they become lethargic. Spend a lot of time at bottom of tank, or hiding. Not eating.
When did you start noticing the symptoms? After about 5 days.
Have you started treating your fish? If so, how? No - just adding variety to diet.
Does your fish have any history of being ill? they've all been new
How old is your fish (approximately)? We've had them a week

I found this information helpful. Hopefully it will help you as well. Also always have a medicine kit on hand for your betta. Yes be prepared. Research the internet for items you should have on hand. It will help save your betta's life.

There is one very important symptom that almost always signals an illness in betta fish: lethargy. Betta fish that act extremely lethargic or lazy may not be getting enough oxygen into their system for one reason or another and may need you to take action in order to improve their health.

The second most important sign that your Betta may be sick is its coloring. If your fish starts to dull in color or lose some of its vibrancy it usually indicates that something is wrong. If you notice a color change in your fish, it may or may not be a disease, sometimes it can be that your fish is stressed. Stress can play a huge role in the health of your fish, so you'll want to eliminate any stress factors that could be influencing your fish. These can include direct bright light on your fish, too small of a living environment, and any constant loud noises that may be too close to its tank. Now once you think that most stress factors can be ruled out; then you can probably assume that your fish is ill.

A common sign of Betta diseases is red-brown lines around your Betta's gills. This generally caused by a chemical imbalance in the water. An increasing level of nitrates in the water can cause the skin around the fills to be deprived of breathable oxygen and pigment. If you see signs of this, you must take action quickly to balance out the water or risk losing your betta fish.

Betta fish diseases have already or are about to spread around the tank if you find your betta fish is gasping for air at the aquarium's surface. This means there is not enough oxygen in your tank. Normally this can be attributed to a build-up of nitrates and/or ammonia. If the water is not properly cycled or not cleaned often enough these toxins can rise to dangerous levels.

One very common Betta disease is parasites. White spots on your Betta's body or fins are an indicator of parasitic infestation. Parasites can quickly affect your fish's immune system and may interfere with its ability to breathe oxygen. There are several aquarium treatments that are designed to fight parasites.

The most deadly mistake can be just a lack of awareness of your fish's health. Make sure you study your Betta daily to ensure that everything is normal. A lot of times owners who do not keep a good eye on their pets health and will only discover something is wrong when it's too late to change anything. The internet is an excellent tool to help find solutions for sick fish. It can also prepare you for every aspect of your Betta fish's life, including the fight against Betta diseases.

To understand...this tank has been setup and running for 2 years with monthly water changes and the newly added Betta become lethargic and die within a few days...correct.....
Did you tear the tank down after the Betta that lived in the tank for 2years or did you just do a water change....

How are you acclimating them to the tank when you first get them...
What kind of filter and filter media care, any live plants-do you have the water pram numbers and what type of test kit used by the pet shop..."Fine" doesn't mean anything.....

Right now-what I would recommend if this is indeed a 2 year old tank with limited water changes.....

First-remove all livestock to QT......then Make massive water changes and deep vacuuming of the substrate....it may be old tank syndrome.....